36 personn working 8 hours a day can do 3 units of working in 12 days. How many persons are required to complete 4 units of that work, if they work 6 hours a day for 16 days?

Options

A. 50
B. 55
C. 48
D. 45

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total work done in terms of person-hours.
Given that 36 persons working 8 hours a day can complete 3 units of work in 12 days, we first calculate the total person-hours used to complete this work.

\[ \text{Total person-hours} = \text{Number of persons} \times \text{Hours per day} \times \text{Number of days} \]
\[ \text{Total person-hours} = 36 \text{ persons} \times 8 \text{ hours/day} \times 12 \text{ days} = 3456 \text{ person-hours} \]

### Step 2: Calculate the work done per unit.
Now, we can find out how many person-hours are required to complete 1 unit of work.

\[ \text{Person-hours per unit} = \frac{\text{Total person-hours}}{\text{Units of work}} = \frac{3456 \text{ person-hours}}{3 \text{ units}} = 1152 \text{ person-hours/unit} \]

### Step 3: Calculate the total work required for 4 units.
Now, we need to find out how many person-hours are required to complete 4 units of work.

\[ \text{Total person-hours for 4 units} = 4 \text{ units} \times 1152 \text{ person-hours/unit} = 4608 \text{ person-hours} \]

### Step 4: Calculate the total available person-hours with the new conditions.
Next, we calculate the total person-hours available with the new conditions where we need to find out how many persons are required to complete the work if they work 6 hours a day for 16 days.

\[ \text{Total available person-hours} = \text{Number of persons} \times \text{Hours per day} \times \text{Number of days} \]
Let \( x \) be the number of persons required.

\[ \text{Total available person-hours} = x \text{ persons} \times 6 \text{ hours/day} \times 16 \text{ days} = 96x \text{ person-hours} \]

### Step 5: Set up the equation and solve for \( x \).
We need the total available person-hours to equal the total person-hours required for 4 units of work.

\[ 96x = 4608 \]

Now, solving for \( x \):

\[ x = \frac{4608}{96} = 48 \]

### Conclusion:
Thus, the number of persons required to complete 4 units of work in the given conditions is **48**.

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